A wire of 10^ -2 kgm^ -1 passes over a frictionless light pulley … - Vidyadip

MCQ

A wire of $10^{-2} kgm^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of wire such that m rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 ms^{^{-1}}$.

A
$M = 5\,\, kg$
B
$\frac{m}{M}$ $=\frac{1}{4}$
✓
$m = 20 \,\,kg$
D
$\frac{m}{M}=4$

✓

Answer

Correct option: C.

$m = 20 \,\,kg$

c
$T=V^{2} M=100 N ; T=m g \sin \theta$

$\mathrm{Mg}=100 \mathrm{N} ; 100=\mathrm{m} \times 10 \times \frac{1}{2}$

$M=10 \mathrm{kg}, \mathrm{m}=20 \mathrm{kg}$

$\frac{m}{M}=2$

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